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We deal with the equations of a planar magnetohydrodynamic compressible flowwith the viscosity depending on the specific volume of the gas and the heatconductivity proportional to a positive power of the temperature. Under thesame conditions on the initial data as those of the constant viscosity and heatconductivity case ([Kazhikhov (1987)], we obtain the global existence anduniqueness of strong solutions which means no shock wave, vacuum, or mass orheat concentration will be developed in finite time, although the motion of theflow has large oscillations and the interaction between the hydrodynamic andmagnetodynamic effects is complex. Our result can be regarded as a naturalgeneralization of the Kazhikhov's theory for the constant viscosity and heatconductivity case to that of nonlinear viscosity and degenerateheat-conductivity.

Global Strong Solutions to Magnetohydrodynamics with Density-Dependent Viscosity and Degenerate Heat-Conductivity